Note. Boxplots display the interquartile range (IQR, center box), and the whiskers extend 1.5*IQR from the lower and upper hinge. The white point indicates the mean and the white center line indicates the median.
Generally, power considerations of mixed effects model such as repeated measures ANCOVAs and multi-level regressions are difficult to estimate because of the complex covariance structures. We ran simulation-studies based on our initial results following the first study. We found that sufficient sample sizes heavily depended on the type and size of the effect. When we simulated models with the marginalization sub-scale (which was the best distributed with mostly small to medium effect sizes), we found that for between-subjects effects, a sample size of 80 participants would have been sufficient (power above .8) with two measurements (see Figure 9 for an illustration). However, for the same between-subject effects we did not reach a power above .8 with any increase of repeated follow-up measurements (based on model extrapolations with a fixed n = 20; tested up to 12 months). The within time effect, on the other hand, was estimated well above .8 by the seventh measurement (i.e., after six months, see Figure 9). The cross-level interaction effects (within-between) were largely a mixture of their individual effects and changes in measurement numbers and sample size affected the models accordingly. We, therefore, urge researchers to rely on pilot data and to run extensive simulation studies to maximize effort and feasibility (i.e., sufficient power).
load("data/S1_Workers/processed/df.btw.RData")
# prepare data for regression (i.e, put into long format and change variable types)
marginalization = melt(df.btw[!is.na(df.btw$assimilation.post),c("marginalization.pre","marginalization.post",
"CtContactNL_c","AvKeyNeedInt_c",
"ExternalReference")],
id=c("ExternalReference","CtContactNL_c","AvKeyNeedInt_c"))
marginalization$time = ifelse(grepl(".pre", marginalization$variable), "pre", "post")
marginalization$variable = gsub(".pre$|.post$", "", marginalization$variable)
marginalization$time = factor(marginalization$time)
marginalization$time = factor(marginalization$time,levels(marginalization$time)[c(2,1)])
marginalization$id = rep(seq(1:20), 2)
Run multilevel regression to extract the effect sizes and covariance matrices
# run regresion
lm.marg <- lmer(value~
AvKeyNeedInt_c*time+
CtContactNL_c*time+
(1|id),
data=marginalization)
summary(lm.marg)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: value ~ AvKeyNeedInt_c * time + CtContactNL_c * time + (1 | id)
## Data: marginalization
##
## REML criterion at convergence: 167
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.743 -0.375 -0.004 0.421 1.428
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 3.268 1.808
## Residual 0.934 0.966
## Number of obs: 40, groups: id, 20
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.2245 0.4690 21.1848 6.87 0.00000082 ***
## AvKeyNeedInt_c -0.0606 0.0395 21.1848 -1.53 0.140
## timepost -0.4957 0.3127 17.0000 -1.59 0.131
## CtContactNL_c -0.0576 0.0415 21.1848 -1.39 0.180
## AvKeyNeedInt_c:timepost 0.0615 0.0263 17.0000 2.34 0.032 *
## timepost:CtContactNL_c 0.0208 0.0277 17.0000 0.75 0.462
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) AvKNI_ timpst CtCNL_ AKNI_:
## AvKyNdInt_c 0.107
## timepost -0.333 -0.036
## CtCntctNL_c -0.202 -0.214 0.067
## AvKyNdInt_: -0.036 -0.333 0.107 0.071
## tmpst:CCNL_ 0.067 0.071 -0.202 -0.333 -0.214
fixef(lm.marg)
## (Intercept) AvKeyNeedInt_c timepost CtContactNL_c AvKeyNeedInt_c:timepost timepost:CtContactNL_c
## 3.22445 -0.06059 -0.49572 -0.05756 0.06148 0.02082
Check post-hoc power for comparison.
# Post-hoc power analysis for single effects (example: key need)
post_hoc <- powerSim(lm.marg, fixed("AvKeyNeed"), nsim=1000)
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post_hoc
## Power [user defined], (95% confidence interval):
## 0.00% ( 0.00, 0.37)
##
## Test: [user defined function]
##
## Based on 1000 simulations, (0 warnings, 1000 errors)
## alpha = 0.05, nrow = 40
##
## Time elapsed: 0 h 1 m 23 s
##
## nb: result might be an observed power calculation
Simulate different participant numbers for all fixed effects.
# extrapolate data:
sim.N <- extend(lm.marg, along="id", n=500)
# Run and plot simulations
plt.pwr.contact = powerCurve(fit = sim.N,
test = simr::fixed("CtContactNL_c", "t"),
along="id",
progress = FALSE,
breaks = seq(10,100,10),
nsim=1000)
plot(plt.pwr.contact) +
title("Outgroup Contact Count [participant numbers]")
## integer(0)
plt.pwr.time = powerCurve(sim.N, simr::fixed("time"),
along="id",
progress = FALSE,
breaks = seq(10,100,10),
nsim=1000)
plot(plt.pwr.time) +
title("Time [participant numbers]")
## integer(0)
plt.pwr.Need = powerCurve(sim.N, simr::fixed("AvKeyNeedInt_c", "t"),
along="id",
progress = FALSE,
breaks = seq(10,100,10),
nsim=1000)
plot(plt.pwr.Need) +
title("Avergage Need Fulfillment [participant numbers]")
## integer(0)
plt.pwr.timeCont = powerCurve(sim.N, simr::fixed("time:CtContactNL_c"),
along="id",
progress = FALSE,
breaks = seq(10,500,50),
nsim=1000)
plot(plt.pwr.timeCont) +
title("Time X Outgroup Contact Count [participant numbers]")
## integer(0)
plt.pwr.timeNeed = powerCurve(sim.N, simr::fixed("AvKeyNeedInt_c:time"),
along="id",
progress = FALSE,
breaks = seq(10,50,5),
nsim=1000)
plot(plt.pwr.timeNeed) +
title("Time X Avergage Need Fulfillment [participant numbers]")
## integer(0)
Simulate different number of within person measurements.
# extrapolate data:
sim.within <- extend(lm.marg, within="id", n=12)
# Run and plot simulations
plt.pwr.t.time = powerCurve(sim.within, simr::fixed("time"),
within="id",
progress = FALSE,
breaks = seq(2,12,1),
nsim=1000)
plot(plt.pwr.t.time) +
title("Time [measurement numbers]")
## integer(0)
plt.pwr.t.contact = powerCurve(sim.within, simr::fixed("CtContactNL_c", "t"),
within="id",
progress = FALSE,
breaks = seq(2,12,1),
nsim=1000)
plot(plt.pwr.t.contact) +
title("Outgroup Contact Count [measurement numbers]")
## integer(0)
plt.pwr.t.Need = powerCurve(sim.within, simr::fixed("AvKeyNeedInt_c", "t"),
within="id",
progress = FALSE,
breaks = seq(2,12,1),
nsim=1000)
plot(plt.pwr.t.Need) +
title("Average Need Fulfillment [measurement numbers]")
## integer(0)
plt.pwr.t.timeCont = powerCurve(sim.within, simr::fixed("time:CtContactNL_c"),
within="id",
progress = FALSE,
breaks = seq(2,12,1),
nsim=1000)
plot(plt.pwr.t.timeCont) +
title("Time X Outgroup Contact Count [measurement numbers]")
## integer(0)
plt.pwr.t.timeNeed = powerCurve(sim.within, simr::fixed("AvKeyNeedInt_c:time"),
within="id",
progress = FALSE,
breaks = seq(2,12,1),
nsim=1000)
plot(plt.pwr.t.timeNeed) +
title("Time X Average Need Fulfillment [measurement numbers]")
## integer(0)
# save simulations, because this takes for freakin ever.
save(plt.pwr.contact,plt.pwr.Need,plt.pwr.t.contact,plt.pwr.t.Need,
plt.pwr.t.time,plt.pwr.t.timeCont,plt.pwr.t.timeNeed,plt.pwr.time,
plt.pwr.timeCont,plt.pwr.timeNeed,
file = "data/S1_Workers/processed/PowerSimPlots.RData")
#load("PowerSimPlots.RData")
The full session information with all relevant system information and all loaded and installed packages is available in the collapsible section below.
| Setting | Value |
|---|---|
| version | R version 4.3.0 (2023-04-21) |
| os | macOS Ventura 13.3.1 |
| system | x86_64, darwin20 |
| ui | X11 |
| language | (EN) |
| collate | en_US.UTF-8 |
| ctype | en_US.UTF-8 |
| tz | Europe/Amsterdam |
| date | 2023-05-19 |
| pandoc | 3.1.1 @ /usr/local/bin/ (via rmarkdown) |
| Package | Loaded version | Date | Source |
|---|---|---|---|
| binom | 1.1-1.1 | 2022-05-02 | CRAN (R 4.3.0) |
| bookdown | 0.34 | 2023-05-09 | CRAN (R 4.3.0) |
| brms | 2.19.0 | 2023-03-14 | CRAN (R 4.3.0) |
| car | 3.1-2 | 2023-03-30 | CRAN (R 4.3.0) |
| carData | 3.0-5 | 2022-01-06 | CRAN (R 4.3.0) |
| data.table | 1.14.8 | 2023-02-17 | CRAN (R 4.3.0) |
| devtools | 2.4.5 | 2022-10-11 | CRAN (R 4.3.0) |
| dplyr | 1.1.2 | 2023-04-20 | CRAN (R 4.3.0) |
| ggpattern | 1.0.1 | 2022-11-09 | CRAN (R 4.3.0) |
| ggplot2 | 3.4.2 | 2023-04-03 | CRAN (R 4.3.0) |
| ggridges | 0.5.4 | 2022-09-26 | CRAN (R 4.3.0) |
| ggthemes | 4.2.4 | 2021-01-20 | CRAN (R 4.3.0) |
| gridExtra | 2.3 | 2017-09-09 | CRAN (R 4.3.0) |
| haven | 2.5.2 | 2023-02-28 | CRAN (R 4.3.0) |
| Hmisc | 5.1-0 | 2023-05-08 | CRAN (R 4.3.0) |
| iterators | 1.0.14 | 2022-02-05 | CRAN (R 4.3.0) |
| kableExtra | 1.3.4 | 2021-02-20 | CRAN (R 4.3.0) |
| knitr | 1.42 | 2023-01-25 | CRAN (R 4.3.0) |
| lme4 | 1.1-33 | 2023-04-25 | CRAN (R 4.3.0) |
| lmerTest | 3.1-3 | 2020-10-23 | CRAN (R 4.3.0) |
| lubridate | 1.9.2 | 2023-02-10 | CRAN (R 4.3.0) |
| Matrix | 1.5-4 | 2023-04-04 | CRAN (R 4.3.0) |
| pander | 0.6.5 | 2022-03-18 | CRAN (R 4.3.0) |
| papaja | 0.1.1 | 2022-07-05 | CRAN (R 4.3.0) |
| pbkrtest | 0.5.2 | 2023-01-19 | CRAN (R 4.3.0) |
| plotly | 4.10.1 | 2022-11-07 | CRAN (R 4.3.0) |
| plotrix | 3.8-2 | 2021-09-08 | CRAN (R 4.3.0) |
| plyr | 1.8.8 | 2022-11-11 | CRAN (R 4.3.0) |
| psych | 2.3.3 | 2023-03-18 | CRAN (R 4.3.0) |
| purrr | 1.0.1 | 2023-01-10 | CRAN (R 4.3.0) |
| RColorBrewer | 1.1-3 | 2022-04-03 | CRAN (R 4.3.0) |
| Rcpp | 1.0.10 | 2023-01-22 | CRAN (R 4.3.0) |
| remedy | 0.1.0 | 2018-12-03 | CRAN (R 4.3.0) |
| reshape2 | 1.4.4 | 2020-04-09 | CRAN (R 4.3.0) |
| RLRsim | 3.1-8 | 2022-03-16 | CRAN (R 4.3.0) |
| rmarkdown | 2.21 | 2023-03-26 | CRAN (R 4.3.0) |
| sessioninfo | 1.2.2 | 2021-12-06 | CRAN (R 4.3.0) |
| simr | 1.0.7 | 2023-04-13 | CRAN (R 4.3.0) |
| stringi | 1.7.12 | 2023-01-11 | CRAN (R 4.3.0) |
| stringr | 1.5.0 | 2022-12-02 | CRAN (R 4.3.0) |
| testthat | 3.1.8 | 2023-05-04 | CRAN (R 4.3.0) |
| tibble | 3.2.1 | 2023-03-20 | CRAN (R 4.3.0) |
| tinylabels | 0.2.3 | 2022-02-06 | CRAN (R 4.3.0) |
| usethis | 2.1.6 | 2022-05-25 | CRAN (R 4.3.0) |
R version 4.3.0 (2023-04-21)
Platform: x86_64-apple-darwin20 (64-bit)
locale: en_US.UTF-8||en_US.UTF-8||en_US.UTF-8||C||en_US.UTF-8||en_US.UTF-8
attached base packages:
other attached packages:
loaded via a namespace (and not attached):